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the escape speed of a projectile on the earth surface is 11.2 kilometre per second a body is projected out with thrice this speedwhatis the speed of the body far away from the Earth ignorance of the sun and other planets

Sudhanva G V , 6 Years ago
Grade 11
anser 1 Answers
Arun

Last Activity: 6 Years ago

Escape velocity of a projectile from the Earth, vesc = 11.2 km/s
Projection velocity of the projectile, vp = 3vesc
Mass of the projectile = m
Velocity of the projectile far away from the Earth = vf
Total energy of the projectile on the Earth = (1/2)mvp2 – (1/2)mvesc2
Gravitational potential energy of the projectile far away from the Earth is zero.
Total energy of the projectile far away from the Earth = (1/2)mvf2
From the law of conservation of energy, we have
(1/2)mvp2 – (1/2)mvesc2  =  (1/2)mvf2
vf = ( vp2 – vesc)1/2
= [ (3vesc)2 – vesc2 ]1/2
= √8 vesc
= √8 × 11.2  =  31.68 km/s.

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